If one were to pick a random integer between 0 and infinity, wouldn't the chance of picking an integer less than infinity be zero?
Infinity is not an integer
The chance of picking infinity would be (approach) zero. But the chance of picking any other one specific integer (such as zero itself) would also be (approach) zero.
>>7701268
Infinity isn't a number.. Even when working with extended reals, when speaking of probability measures, and consequently probability measures, the set where a RV takes on the value + infinity or -infinity has measure 0...
Also, see Kai Lai Chung's book on measure theoretic probability.. Picking a random integer doesn't quite make sense in the case to which you're referring.. I'm assuming you want all integers to be equally likely. There's no uniform distribution for infinite discrete sets.
>>7701268
It is 0 if you talk about a uniform distribution. Which is ill defined for infinite sets, unless you have something on your mind.
You could also use a distribution p(n) =1/2^(n+1) for non negative n.
>>7701268
The probability of picking any particular number is indeed zero (assuming the probability distribution is uniform).
>>7701268
Friends, assume a uniform probability distribution and pick any one integer at random.
The probability of picking any one specific integer is 0.0... = 0, yes?
x * 0 = 0, yes?
Which means the probability sum of any integer being picked at all is 0, yes?
Which is clearly absurd, since picking one was the very premise.
Yet, this same clearly absurd logic supposedly "proves" 0.9... = 1.
Limits are an oversimplification. 0.9... != 1.
There isn't an uniform probability distribution on any countable set A.
>>7701325
Doesn't matter.
Probability of picking any integer n is 1 / infinity = 0.0... = 0
The natural choice for a probability distribution on the non-negative integers would be the Poisson distribution. A Poisson distributed random variable is almost surely finite.
>>7701330
Please take math 101 and then come back here. The distribution p(n)=1/2^n works perfectly.
>>7701330
Division by infinity is not defined.
Wouldn't it be 1?
following the premises that i) both 0 and infinity themselves cannot be picked and ii) upon the picky of any integer it'd <infinity by default?
>>7701279
>would be (approach)
Being zero and approaching zero are not the same thing. Otherwise, you could argue that 1/0 = infinity since 1/x approaches infinity as x approaches zero. I mean I get what you're saying, it's "effectively" a zero chance, but it's not strictly correct.
>>7701268
I'm very late, but yes, infinity is not an integer, it is an idea - a concept. It does NOT represent a number in any way.
>>7701268
Do you mean the chance of picking a SPECIFIC integer? It wouldn't quite be zero, it would be the smallest number above zero, which I suppose you could call "positive minimum infinity" (whereas "normal" infinity is "positive maximum infinity").
>>7701383
No. Infinity does not represent a number. Saying "positive maximum infinity" makes no sense.
You can't if you give each number the same finite probability. The reason is that all the probabilities have to add up to 1 (or at least some finite number) and every infinite series over a constant number diverges (i.e goes to infinity).
You can however give a non-uniform distribution like 1/2^n which summed up gives 2 and hence lets you define a probability.
>>7701348
Why would it have to be defined?
>>7701380
p(n) = 1 / N
As N approaches infinity, p(n) approaches 0.0... = 0, so the limit gives you p(n) = 0. Or an infinite number of impossible possibilities, i.e. no possible outcome. Clearly that's absurd.
I'm NOT contending p(n) = 0.
I'm contending 0.9... != 1.0 by reductio absurdum.
>>7701402
>Why would it have to be defined?
Because every mathematical operation needs to be defined.
what's infinity - 1?
>>7701421
That's like asking "what's bob - 1"
It's undefined. Infinity is NOT a number.
>>7701408
We're talking about limits and how they oversimplify.
1 / infinity being undefined is irrelevant unless you ignore context and sperg out. You're not being asked to peer review a paper.
>>7701433
No it's not irrelevant. You're trying to calculate probabilities for "infinite elements" and applying maths that is only defined for finite elements. You're completely wrong here.
>>7701431
so can we accept the premise that by definition any integer picked would have to exist to a group of real, quantifiable values, all of which <infinity and would therefore yield a probability of 1?
tell me if im wrong
>>7701446
[math]p_{N}(n) = \frac{1}{N}[/math]
[math]\lim_{N \to \infty} \frac{1}{N} = 0[/math]
happy?
>>7701357
Go ahead and try to construct a uniform probability measure on the positive integers.
Intuitively it makes no sense.. Just think of what is being done here... You don't need anything but the Archimedean principle to see that this can't be done unless everything is uniformly assigned 0, in which case, we don't have a probability distribution.
Suppose there exists some positive number k such that
P(n)=k for each positive integer n. Intuitively, k should be very small if this is to work.
By the archimedean principle, there exists a M such that
Mk = P({1,2,....,M})=P({1})+...+P({M}) > 1..
We no longer have a probability distribution.
Excuse my lack of LaTex, but I hate Tex-ing in 4chan.
>>7701602
So.. We've reached a contradiction here.. Thus, we conclude no such k exists. Tah-Dah..
If you want to discuss any deeper you'll need to study actual probability theory. There are much deeper philosophical discussions than this that come from it.
>>7701380
>Being zero and approaching zero are not the same thing
1-1 Infinitesimal
>>7701380
Be careful, buddy.
You couldn't argue that 1/0= infinity because
this is only true from the RHS.. What happens if you approach zero from the left?
>>7701268
>an integer less than infinity
what does that even mean?
>>7701624
I assume his set includes all non-negative integers and ends with a hypothetical element "infinity".
>>7701656
exactly, infinity = 2
>>7701656
*with both 0 and infinity being excluded from the list of possible values
>>7701661
as in probability
as in uh
if his set includes all non-negative integers and both 0 and infinity are excluded from this range of possibilities (up to and including infinity - 1) then the possibility of a number being picked from this list and <infinity = 1
?
>>7701671
because otherwise it doesn't make sense
wtf are we even discussing at this point. we don't even know what we're arguing over anymore
>>7701680
It's the only way I can make any sense of the OP.
"Almost surely" and "Almost never" are acknowledged as terms in probability
https://en.wikipedia.org/wiki/Almost_surely
The chance of picking a given integer from the set of all integers is not zero. It's just almost zero.
>>7701681
do you believe in life after love?
>>7701692
What a convenient cop-out.
Then, let's also agree 0.9... is almost 1.
Could you not argue similarly that the probability of picking any value <1 between 0 and 1 (including 0.1.. to 0.9..) is equal to 1 despite there being an infinite number of values between those 2 limits?
Conversely, despite there being an infinite variation of possibilities approaching infinity, and excluding infinity itself, wouldn't the probability governing the prospect of landing on one of these values work in a simiar sense?
, following the premise that the largest possible value that can be picked works as infinity - 1 and existing to the set of quantifiable positive integers
>>7701276
neither is 0.
>>7702212
0 is in the set of integers
>>7701268
it is, the probability of n individual item of a continuous set is always 0. This doesn't meant it can't happen, just extremely unlikely.
>>7701318
>Which means the probability sum of any integer being picked at all is 0, yes?
no.
>>7702236
the integers are countable so it is not possible to give them all probability 0
The uniform[1,...,N] random variables do not converge to anything
>>7701494
That doesn't prove anything about your original proposition though.
>>7701283
/thread
why did you all keep replying t-bh
Y'all who think there exists a uniform probability distribution over a countable set are retarded and should feel bad
What is the probability that choosing a non negative integer is not an integer? Wouldn't that be 0? Wouldn't that mean the answer to OPs question is 1?
>>7702321
>probability that an integer is not an integer
>>7702325
Can such a statement not be assigned a probability? I'm serious. I don't know much about measure theory and all that.
>>7702331
yeah it can I guess, but it's obviously 0 anyway
OP's question and reasoning doesn't make sense anyway, and it's difficult to see the link to your comment
